A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
Let V be the volume of the sphere, then
Therefore, Rate of change of volume (V) with respect to its radius (r) is given by,
…….. by chain rule
Thus, when r = 10cm
Then, 
Therefore, the rate at which its volume is increasing with the radius when the later is 10 cm is 400π cm3/s.
9